## Vector Calculus, Fourier Series and Fourier Transforms

This book on ‘Vector Calculus, Fourier Series and Fourier Transforms’ has been designed as a text-book for B.Sc. Mathematics Major of Madras University. The subject matter presented in this book fully covers the revised syllabus prescribed for paper 7 in the fourth semester.
In the preparation of the chapters in this book, a knowledge of mathematics at the plus two levels is assumed.

In all the chapters, fundamental concepts are explained and a number of illustrative examples have been .worked out. Past examination question papers have been given for the benefit of the students, along with Model question papers as per the revised pattern under the semester system. It is very _much hoped that this book will be found useful by all those for whom it is meant. Suggestions for improvement of this book will be gratefully acknowledged.

## Quantitative Aptitude Fully Solved Book for Competitive Examinations

Quantitative Aptitude For Competitive Examinations comprehensively covers topics for the Quantitative Aptitude and Data Interpretation section of competitive exams like management entrance exams, job recruitment exams etc.Competitive exams, whether they are conducted to select candidates for jobs, or for admission to post graduate and doctorate courses, test the numerical aptitude of the person taking the exam. These exams test a candidate’s knowledge and skill in basic arithmetic, algebra, geometry etc. They also test the Quantitative Aptitude skills of the candidate. This book is divided into two sections. The first part covers arithmetical ability.

The second part covers the Data Interpretation. The first part begins by taking a look at Numbers, Average, Percentage, Decimal Fractions, H.C.F. and L.C.M., Square Roots, and Cube Roots. Quantitative Aptitude For Competitive Examinations also covers Problems on Numbers and Ages, Simplification, Alligations, and Logarithms. Other topics discussed include Surds and Indices, Pipes and Cistern, Chain Rule, Boats and Streams, Simple and Compound Interests, Time and Work, Partnership, Problems on Trains, and Volume and Surface Area.

This text also goes into Stocks and Shares, True Discount and Banker’s Discount, Games of Skill, Races, Permutations and Combination, Series, Odd Man Out, Clocks, Heights and Distances, and Calendar. The Data Interpretation part covers Tabulation and various kinds of graphs like Bar, Pie, and Line Graphs. Quantitative Aptitude For Competitive Examinations covers every aspect of the numerical ability section of many competitive tests. Numerous examples have been used throughout the book to illustrate the concepts and problem-solving techniques. This book gives the students or candidates a good idea about the kind of questions asked in these exams.

An ideal book for Bank PO, SBI-PO, IBPS, RBI Exams — MBA, MAT, CMAT, GMAT, CAT, IIFT, IGNOU — SSC Combined Preliminary Exams, Hotel Management — Sub-Inspectors of police, CBI, COP Exams — UPSC-CSAT, SCRA, and other State Services Exams — Railway Recruitment Board Exams — Campus Recruitment Tests.

## Numerical Methods: Problems and Solutions

About the Book: This comprehensive textbook covers material for one semester course on Numerical Methods (MA 1251) for B.E./ B. Tech. students of Anna University. The emphasis in the book is on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner. The book is written as a textbook rather than as a problem/guide book. The textbook offers a logical presentation of both the theory and techniques for problem solving to motivate the students in the study and application of Numerical Methods. Examples and Problems in Exercises are used to explain.

This book is based on the experience and the lecture notes of the authors while teaching Numerical Analysis for almost four decades at the Indian Institute of Technology, New Delhi. This comprehensive textbook covers material for a one-semester course on Numerical Methods of Anna University.

The emphasis in the book is on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner. The book is written as a textbook rather than as a problem/guide book. The textbook offers a logical presentation of both the theory and techniques for problem-solving to motivate the students for the study and application of Numerical Methods.

Examples and Problems in Exercises are used to explain each theoretical concept and application of these concepts in problem-solving. Answers for every problem and hints for difficult problems are provided to encourage the students for self-learning. The authors are highly grateful to Prof. M.K. Jain, who was their teacher, colleague, and co-author of their earlier books on Numerical Analysis. With his approval, we have freely used the material from our book, Numerical Methods for Scientific and Engineering Computation, published by the same publishers. This book is the outcome of the request of Mr. Saumya Gupta, Managing Director, New Age International Publishers, for writing a good book on Numerical Methods for Anna University. The authors are thankful to him for following it up until the book is complete.

The first author is thankful to Dr. Gokaraju Gangaraju, President of the college, Prof. P.S. Raju, Director and Prof. Jandhyala N. Murthy, Principal, Gokaraju Rangaraju Institute of Engineering and Technology, Hyderabad for their encouragement during the preparation of the manuscript. The second author is thankful to the entire management of Manav Rachna Educational Institutions, Faridabad, and the Director-Principal of Manav Rachna College of Engineering, Faridabad for providing a congenial environment during the writing of this book.

## Microeconomics: Theory And Applications

Description This book is intended to be a comprehensive and standard textfor undergraduate students of Microeconomics. Not only this bookprovides students with sufficient study material for theexamination purpose, it aims at making them understand economics. Complex theories are explained with self-explanatory diagrams Real examples are given to explain microeconomic theories Plenty of numerical examples Each chapter begins with learning objectives Questions of various universities are given at the end of each chapter Introduction to Microeconomics The Economy: Its basic problems and working system The Market forces Demand and Supply Elasticity of Demand and Supply Application of Market Laws and Elasticity Theory of Consumer Demand: Cardinal Utility Approach Theory of Consumer Demand: Ordinal Utility Approach Application Indifference Curve Analysis Revealed Preference Theory Consumer Surplus Theory of Production: Laws of Returns to Variable Input Theory of Production: Laws of returns to a Variable Input Optimim Combinations of Inputs Theory of Costs The Objectives of Business Firms and their market Powers Price and Output Determination under Perfect Competition Price and Output Determination under Monopoly Price and Output Determination under Monopolistic Competition Price and Output Determine Oligopoly The Factor Market: Factor Demand and Supply Wage Determination under Perfect Competitions Wage and Employment Determination under Imperfect Competition Theory of Rent Theories of Interest and Investment Decisions Theories of profit Product Exhaustion Theorem General Equilibrium Analysis Welfare Economics:

This book is intended to be a comprehensive and standard textbook for undergraduate students of Microeconomics. Apart from providing students with sufficient study material for examination purposes, it aims at making them understand economics. An effort has been made to explain abstract and complex microeconomic theories in a simple and lucid language without sacrificing analytical sophistication. The subject matter has been structured in a systematic manner without leaving gaps for the readers to fill in. Though the approach is non-mathematical, simple algebra has been used to give a concrete view of economic concepts and theories and to show the applicability of economic theories in decision making.« Less

## Introduction to Mathematical Statistics

introduction to Mathematical Statistics is a comprehensive book for undergraduate students of Physics and Mathematics. The book comprises chapters on probability and distributions, multivariate distributions, maximum likelihood methods, and is a comprehensive book for undergraduate students of Physics and Mathematics. The book comprises chapters on probability and distributions, multivariate distributions, maximum likelihood methods, and Bayesian statistics. In addition, the book consists of chapter-wise questions and practice exercises to help understand the concepts better. This book is essential for students of math preparing for competitive examinations like IIT-JAM and NET.

this seventh edition, our goal has remained steadfast: to produce an outstanding text in mathematical statistics. In this new edition, we have added examples and exercises to help clarify the exposition. For the same reason, we have moved some material forward. For example, we moved the discussion on some properties of linear combinations of random variables from Chapter 4 to Chapter 2. This helps in the discussion of statistical properties in Chapter 3 as well as in the new Chapter 4.

One of the major changes was moving the chapter on “Some Elementary Statistical Inferences,” from Chapter 5 to Chapter 4. This chapter on inference covers conﬁdence intervals and statistical tests of hypotheses, two of the most important concepts in statistical inference. We begin Chapter 4 with a discussion of a random sample and point estimation. We introduce point estimation via a brief discussion of maximum likelihood estimation (the theory of maximum likelihood inference is still fullly discussed in Chapter 6).

In Chapter 4, though, the discussion is illustrated with examples. After discussing point estimation in Chapter 4, we proceed onto conﬁdence intervals and hypotheses testing. Inference for the basic one- and two-sample problems (large and small samples) is presented. We illustrate this discussion with plenty of examples, several of which are concerned with real data. We have also added exercises dealing with real data. The discussion has also been updated; for example, exact conﬁdence intervals for the parameters of discrete distributions and bootstrap conﬁdence intervals and tests of hypotheses are discussed, both of which are being used more and more in practice. These changes enable a one-semester course to cover basic statistical theory with applications. Such a course would cover Chapters 1–4 and, depending on time, parts of Chapter 5. For two-semester courses, this basic understanding of statistical inference will prove quite helpful to students in the later chapters (6–8) on the statistical theory of inference.

## Topics in algebra

Topics in Algebra with a certain amount of trepidation. On the whole, I was satisfied with the first edition and did not want to tamper with it. However, there were certain changes I felt should be made, changes which would not affect the general style or content, but which would make the book a little more complete. I hope that I have achieved this objective in the present version. For the most part, the major changes take place in the chapter on group theory.

When the first edition was written it was fairly uncommon for a student learning abstract algebra to have had any previous exposure to linear algebra. Nowadays quite the opposite is true; many students, perhaps even a majority, have learned something about 2 x 2 matrices at this stage. Thus I felt free here to draw on 2 x 2 matrices for examples and problems. These parts, which depend on some knowledge of linear algebra, are indicated with a #. In the chapter on groups I have largely expanded one section, that on Sylow’s theorem, and added two others, one on direct products and one on the structure of finite abelian groups.

In addition to the proof previously given for the existence, two other proofs of existence are carried out. One could accuse me of overkill at this point, probably rightfully so. The fact of the matter is that Sylow’s theorem is important, that each proof illustrates a different aspect of group theory and, above all, that I love Sylow’s theorem. The proof of the conjugacy and number of Sylow subgroups exploits double cosets. A by-product of this development is that a means is given for finding Sylow subgroups in a large set of symmetric groups.

## Discrete Mathematical Structures with Applications to Computer Science

The purpose of this text is to present an integrated treatment of a number of those topics in mathematics which can be made to depend only upon a sound course in elementary calculus, and which are of common importance in many fields of application. An attempt is made to deal with the various topics in such a way that a student who may not proceed into the more profound areas of mathematics may still obtain an intelligent working knowledge of a substantial number of useful mathematical methods, together with an appropriate awareness of the foundations, interrelations, and limitations of these methods. At the same time, it is hoped that a student who is to progress, say, into a rigorous course in mathematical analysis will be provided, in addition, with increased incentive and motivation in that direction, as, for example, when he is confronted by the phrase HIt can be shown” within the derivation of a useful concrete result, or when he has led to a sense that a certain new concept is a fertile one and is deserving of being expanded and made more precise.

The book is a revision of Advanced Calculus for Engineers, published in 1949, incorporating not only a number of minor changes for the purpose of increased clarity or precision but also some added textual material, as well as a very substantial number of additional problems. The first four chapters are concerned chiefly with ordinary differential equations, including analytical, operational, and numerical methods of solution, and with special functions generated as solutions of such equations. In particular, the material of the first chapter can be considered as either a systematic review or an initial introduction to the elementary concepts and techniques. associated with linear equations and with special

solvable types of nonlinear equations, which are needed in subsequent chapters. The fifth chapter deals with boundary-value problems governed by ordinary differential equations, with the associated characteristic functions, and with series and integral representations of arbitrary functions in terms of these functions. Chapter 6 develops the useful ideas and tools of vector analysis; Chapter 7 provides brief introductions to some special topics in higher-dimensional calculus which are rather frequently needed in applications. The treatment here occasionally consists essentially of indicating the plausibility and practical significance of a result and stating conditions under which its validity is rigorously established in listed references. 